Using vector method, prove that in a triangle, `a^(2)=b^(2)+c^(2)-2bc" "cosA` (cosine law).

Using vector method prove that in any triangle ABC a^2=b^2+c^2-2bc cos A .

Prove by vector method, that in a right-angled triangle ABC, AB^(2) + AC^(2) = BC^(2) , the angle A being right angled. Also prove that mid-point of the hypotenuse is equidistant from vertex.

In a triangle ABC, using vector prove that c^(2)=a^(2)+b^(2)-2abcosC

A, B, C and D are four points in space. Using vector methods, prove that AC^(2)+BD^(2)+AC^(2)+BC^(2)geAB^(2)+CD^(2) what is the implication of the sign of equality.

Show by vector method that sin 2A=2sin A cosA .

Using vector method, prove that the following points are collinear: A(1,2,7) B(2,6,3) C(3,10,-1)

Using vector method, prove that the following points are collinear: A(-3,-2-5),B(1,2,3)and C(3,4,7)

Using vector method, prove that the following points are collinear: A(2,-1,3) B(4,3,1) C(3,1,2)

Prove that in triangle A B C ,cos^2A+cos^2B-cos^2C=1-2sinAsinBcosCdot

Prove that : (sinA+cosA)^(2)+(sinA-cosA)^(2)=2